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Calculations guide
Introduction Calculations, or “calcs” for short, are fan quantification of feats that happen in a certain series. They try to apply real life physics formulas in order to attain a grasp of a certain character or series power levels. Calculations are split to different types varying in their levels of difficulty depending on how hard it is to attain the result. Calcs, like everything, are subject to acceptance and denial. Calcs that their math, scaling and science is checked to be at least 99% accurate are called "accepted calcs". Said calcs are what's used in Vs debates. Calcs are also subjected to be outliers for a certain character or characters and as such must be dealt with with care. It's usually a good idea for a group to have their own "experienced calculators" that can identify whether a calc could be accepted or not. However, everyone can become an "experienced calculator" just with a bit of hard work. Types of calculations There are two different types of calculations; speed and DC (Short for destructive capacity). Speed calcs utilize the standard formula for velocity (V= d/t where d is the distance and t is the time frame). They are widely considered to be the second easiest calc type due to its clarity of application. DC calcs, however, is where things get tricky. DC is arguably the second most important stat for a character to have so getting a clear result of it is essential. DC calcs use the energy of the attack as a basis which is measured in Joules or their respective tnt equivalent (preferably the latter as it is more easily understood). Energy can be quantified from a variety of laws each differing from the other (Ex. Stephan-boltzmann’s law of radiation, volume destruction of the matter, Kinetic energy, potential energy, gravitational binding energy, etc). Each of the aforementioned laws is used depending on the exact nature of the feat. Forms of media As there is different types of calcs, there are different forms of media each with their own special rule regarding calcs. #Motion pictures (Anime, TV series, movies and cartoons): Those are the easiest types of series to quantify due to their nature of providing a time frame and a size approximation due to either story boards, concept art, real life actors and items. Time frame in motion pictures is measured using either timers or frame capture methods. # Comics/manga/manhwa: Those are the second type of series in terms of difficulty to quantify. The reasons for that being that the time frame isn’t usually provided by the source material and that different artists draw differently. #Games: The third hardest form of media. It mixes elements from both motion pictures and comics, but its downside lies with game mechanics and how someone can differentiate them from actual feats. #Novels (Light, visual and normal): The absolutely hardest form of media to quantify. Novels, most of the time, don’t provide information regarding feats. Also, many utilize hyperbole, artistic liberties, translator liberties and assumptions. Caution must be taken when dealing with novel feats as to not “lowball” or “wank” a feat Basic tools Pixel scaling The most basic skill of a calculator. It’s used to measure the dimensions of a certain object by utilizing its pixeled dimensions and a ratio that can obtained from another object near it that has a known/approximated size. How to pixel scale #Open MS paint #Get the image #Select the “line” tool and select a color #Draw a line from the “bottom” of the object to the “top” #You’ll see two numbers in the bottom of the screen. Those designate the X and Y length of the object’s size #Apply X and Y to the formula (X^2+Y^2)^0.5 to get the pixel height/width #Get the height/width of the known object in meters #Get the ratio (Ratio = height in meters/height in pixels) #Repeat steps 3-6 and get the height/width of the unknown object in pixels #Multiply the ratio by the height of the unknown object in pixels = Notes: = #Pixel scaling isn’t without its flaws. One of them being inaccuracy of measurement. This can be treated by using the highest possible images quality. #Two people can’t scale the same hence there would always be a margin of difference between different calculators. If the margin is 1-2%, then the pixel scaling is accurate. #Always scale objects that are in close proximity. Never scale objects that are more than (10*known object height) from each other. However, this rule doesn’t always apply as it depends on how writers/artists draw their panels. Angular sizing (Angsize) the second most elementary tool of a calculator. It’s used to calculate the distance an object of known size is from the screen. It’s more commonly used in speed calcs. How to Angsize. #Get the desired object’s height in pixels #Get the panel HEIGHT in pixels. #Apply to the formula 2*atan((Object height/panel height)*tan35) and get the angle of the object #Apply the angle of the object to the calculator here. #Make sure that you select Distance and Degrees. = Notes: = * You can also get the distance without using the calculator by applying the formula. Distance to object = Object size (in meters)/2/ ((Object height/panel height)*tan35) * You can get the distance between two objects by getting both of their distance to the screen and then deducting the results. Speed calculations As mentioned above, speed is the second easiest type of calc to do. It merely uses the distance and the time frame of crossing said distance. Usually, a time frame is either provided (in case of games and motion pictures), assumed (in case of travel speeds and combat speeds. Assume time frames generally have a low end and a high end), or calculated from another object moving in the direction of the character (reaction speed). Out of all the aforementioned ones, reaction speed is the hardest. To calculate reaction speed, you need the time frame for that the dodge occurred in. The time frame can be calculated by dividing the distance that the projectile crossed by its speed. Examples: 1) a character flies around the earth in 3 seconds (motion picture time frame captured using the frames method) * Earth’s circumference = 40030173.592 meters (approximately) * Time frame = 3 seconds * Speed = Distance/time * Speed = 40030173.592/ 3 * Speed = 13343391.197 m/s 2) A character runs from the north pole to the south pole. Time frame not specified but implied to be small. * Distance crossed = half of the earth’s circumference = 20015086.796 meters (approx) * Time frame (low end) = 1 minute * Time frame (high end) = 5 minutes * Speed (low end) = 333584.77 m/s * Speed (high end) = 66716.9559 m/s 3) A character dodges a projectile by 2 meters. The projectile moves at the speed of sound and was fired from 10 meters away. * Speed of the projectile = 340 m/s * Distance that the projectile traveled = 10 meters * Time frame = Distance that the projectile traveled/projectile speed * Time frame = 0.0294 seconds * Distance that the character moved = 2 meters * Character’s reactions speed = distance that the character moved/time frame * Character’s reactions speed = 68 m/s = Notes = * Magical light, lightning and sound's speeds do not equate to their real life respective counterparts unless they were either channeled (in case of lightning) or were stated to be as fast as the real thing. DC calculations''' As already discussed, DC has many different laws, formulas and values that it can be calculated from. They are as follows in order of difficulty: Destruction of matter This is the easiest type of calculations to do. You simply need the destroyed matter’s volume in cubic centimeters (cc) and then multiply the volume by the appropriate value for fragmentation, violent fragmentation, pulverization, vaporization, atomization and –very rarely- sub-atomic destruction. * Fragmentation value = 8 j/cc * Violent fragmentation value = 69 j/cc * Pulverization value = 214.35 j/cc * Vaporization value = 25700 j/cc The table below describes the values used for cement, concrete, ice and the human body which are the most common materials in fiction. (credits to Iwandesu and Fluttershy for the values) Notes: *Fragmentation is used when there are large chunks of the destroyed matter laying around. *Violent fragmentation is for when the matter has been destroyed into tiny pebble-sized pieces. *Pulverization is for when the matter is “grinded” and reduced to an indistinguishable state similar to dirt. *Vaporization is for when the matter is visibly vaporized (mostly by heat-based attacks). It’s also used when there’s dust visible in the panel/screen. *Atomization is used only when stated *Sub-atomic destruction is used only when stated Nuke Used when there’s a large explosion on a planet and there’s no visible crater left. Simply get the radius of the explosion and then go the calculator here. Keep inserting values in megatons until the “Air blast radius near total fatalities” = explosion’s radius. Stardestroyer calculator is the go-to calculator for feats of this sort. Kinetic energy Very standard and self-explanatory. Simply get the mass of the object (Usually requires scaling the object’s dimensions, getting the volume and then multiplying the volume by the density of the object) and the speed of the object (Either use a standard speed like the ablation speed, escape velocity or meteor velocity in case of meteors or assume a time frame and calculate the speed based on said time frame as long as the time frame assumed is lowball) then solve the equation: '''KE = 0.5*m(mass of the object)*V2 (velocity squared) (for non relativistic speeds) KE = (0.5*m*v2)/(1-(v2/c2))^0.5 (for relativistic speeds) Where: m: the mass of the object v: velocity (speed) c: speed of light = Notes = *Kinetic energy isn’t used for characters moving at certain speeds (example of a fallacious KE calc: This character moves at 0.9c so that means he/she is country level via KE of moving his body at such speed) Potential energy The energy of lifting an object/objects a certain distance from the planet. It’s a pretty simple equation that merely requires the mass of the object (can be acquired in the same way as in KE) and the altitude of the object. The gravitational accelaration is usually earth’s (9.8 m/s^2) unless the planet’s gravitational constant is stated to be greater (example: planet Vegeta having 10 g). PE '''(Also called GPE as in gravitational potential energy) = m*g*h''' (in case of objects close to the ground) PE = ((G*M*m)/R – (G*M*m)/r) (in case of objects really far from the surface) Where: m: object’s mass g: gravitational acceleration G: gravitational constant (6.674e-11) M: mass of the planet R: altitude of the object+ the planet’s radius r: the planet’s radius Heat and change of states This method is used when an object is visibly heated/cooled to a certain degree (via statement) or until it changes states (Solid to liquid). Most of the time, it involves water. The most basic thing to understand about this is that there are standard temperatures that are used in these types of calcs. These are room temperature (25 C) and ice temperature (-10 C). Objects that change states from one to another must reach these temperatures at the very least. Heat depends on the specific heat of the matter (which is usually water), mass and delta(t) (the change in temperatures). Q = m*C*Delta(t) Where: Q: energy m: mass of the object C: specific heat of the object Delta(t): change in temperature The change in temperature is measured only until the material’s melting/freezing/evaporating/condensing points. After reaching that point, you’d need to apply the appropriate formula for the state change. Q = m*L Where: Q: energy m: mass of the object being subjected to heating L: the fusion/evaporation latent heat of the object After reaching the appropriate temperature and conversion of matter to the required states, the total energy is the sum of Q. Radiation (heat) an advanced calc method. It relies on the Stephan-blotzmann law of radiation (every object above 0 Kelvin radiate energy). It can be calculated using the formula: P = A*(Stephan-boltzmann constant)*T^4 Where: P: Power (measured in watts. One second is used as the time frame hence the value of P = E) A: the surface area of the object (usually the character’s body surface) Stephan-blotzmann constant: self-explanatory. 5.67e-8 T: Temperature = Notes: = *In DC calculations, the surface area A is that of the attack’s origin (Usually the hand or a flaming ball) *In Durability calculations, the surface area is that of the character’s entire body. Average surface area of humans is 1.9 m^2. Radiation (light) This type of calculation is divided into two sub-types; Radiation of light over a small area (less than one astronomical unit) and radiation of light over a large area (more than one parsec). Radiation over a small area It uses the standard formula of area of sphere and then multiply the area (in cm^2) by the values for human eye’s luminance threshold (200-400 joules/cm^2) whereas 200 joules/cm^2 is the value used when the light is strong enough to sting, but not burn, the human and 400 joules/cm^2 is the value used when the light is strong enough to burn the eye. E (low end) = A*200 E (high end) = A*400 Where: E: energy of radiation A: surface area of the sphere of radiation measured in cm^2 Radiation over a large area It uses the absolute and apparent magnitude of the explosion to measure the explosion’s total radiation power. This method also relies on the luminance of the explosion. Luminance can be described as the intensity of light emitted from a surface in a certain direction. This method of calculation is considered among the hardest so I’ll be detailing the method step by step. How to calculate radiation of light over a large area. Step 1: Determine the luminance of the explosion using either valid assumptions or character statements. Step 2: Calculate the apparent magnitude of the explosion using the following equation m = (-2.5*Log(luminance)) – 14.2 Where: m: apparent magnitude of the explosion Luminance: self-explanatory Step 3: Determine the distance that the explosion reached (in parsecs) Step 4: Calculate the absolute magnitude of the explosion using the following equation M = m+5 – (5*Log(distance)) Where: M: the absolute magnitude of the explosion m: the apparent magnitude Distance: self-explanatory. Measured in parsecs. Step 5: Calculate the luminosity of the explosion using the following formula Luminosity = n^(4.83-M) Where: n: fifth root of 100 (2.511886 approximately) M: the absolute magnitude of the object Step 5: Multiply the resultant luminosity by the luminosity of the sun (3.86e26 watts) P = resultant luminosity*Sun’s luminosity Step 6: Divide the total power by the time frame (or assume a 1 second time frame in case a solid time frame is not available) = Notes = *Luminance of a white light explosion is a standard 66,000 lux Earthquakes’ energy quakes are one of the most common tropes in animanga that are used to hype a character’s strength however, not all quakes are to be considered into calculation. Unless the “shaking” was stated by characters that it resembles an earthquake or if the context of the situation compels so. As is the case with radiation of light, earthquakes are one of the trickiest feats to calculate so I’ll be detailing the method, again, step by step. How to calculate the energy of an earthquake Step 1: Set up a nanogram (example below) Step 2: Calculate the distance between the epicenter and the hypocenter (also called Focus). The hypocenter being the point of the quake’s origin. The epicenter is the point on the surface of the earth above the hypocenter. (see picture below). Most quakes feats are shallow quakes that happen directly on the surface so the epicenter = the hypocenter and the distance between them becomes 0. Step 3: determine the scale of the quake on the Richter scale. Most quakes are 4.5 (Quakes that shake the ground without major damage). Quakes that cause volcanic eruptions are 8.6 (The same as the quake that cause mt Fuji to erupt). Step 4: Draw a line from the distance bar across the scale bar until you reach the amplitude value. If the nanogram doesn’t have the values for amplitude that you want. Simply pick a lower value of richter scale (instead of 4.5. make it 3.5 or 2.5) and draw a line from the distance to the amplitude then multiply the value of amplitude by 10^(difference between the two Richter scales) (example: drawing from 0 to 4.5 isn’t possible so I’d draw to 2.5. The difference between 4.5 and 2.5 is 2. Multiply the amplitude by 10^(4.5-2.5) = 100.) Step 5: determine the distance from which the quake occurred in miles then divide the outcome by 5.7 to get the time that the quake traveled. Delta(t) = Distance/5.7 Where: Delta(t): time in seconds Distance: in miles Step 6: Calculate the magnitude of the quake by solving the equation below: M = Log(amplitude)+3*Log8*delta(t)-2.92 Where: M: magnitude of the earthquake. Amplitude: determined using the nanogram. Delta(t): time Step 7: Plug the magnitude into the calculator here or calculate the energy YOURSELF! Using the formulas below: R = (2/3)*Log(E/Eo) Where: R = M: the magnitude E: energy of the quake in joules Eo: energy of a reference quake which equates to 10^4.8 joules TNT equivalent, sound speed and other calculation info TNT equivalent As the name implies, TNT equivalent is the amount of TNT required to produce the same explosive energy as a certain feat. It's a very common concept in calcs to convert the result into into TNT equivalent. To convert to TNT equivalent, simply divide the result of the calc by a factor of 4.184e9. You'd get the equivalent in TNT tons. After that, simply divide the resultant TNT tons by the appropriate magnitude (to the nearest 3) and add the appropriate prefix. * 1 ton of TNT = 4.184e9 joules * 1 kilotons of TNT = 4.184e12 joules * 1 megaton of TNT = 4.184e15 joules * 1 gigaton of TNT = 4.184e18 joules * 1 teraton of TNT = 4.184e21 joules * 1 petaton of TNT = 4.184e24 joules * 1 exaton of TNT = 4.184e27 joules * 1 zettaton of TNT = 4.184e30 joules * 1 yottaton of TNT = 4.184e33 joules * 1 ninaton of TNT = 4.184e36 joules * 1 tenaton of TNT = 4.184e39 joules Sound speed (Mach) In the Vscommunity, speed is usually measured in mach, which equates to the speed of sound (340 m/s) due to its ease of conversion and its convenience. See the Speed page for more info. Standard speeds used in this Wiki's calculations * Speed of light = 299,792,458 m/s (881,742.52 mach) * Speed of sound = 340 m/s (1 Mach) * Speed of lightning (low end) = 98,327.7778 m/s (289.199 Mach) * Speed of lightning (high end) = 150,000 m/s (441.176 Mach) * Ablation speed (low end) = 2000 m/s * Ablation speed (high end) = 4000 m/s * Earth’s escape velocity = 11200 m/s (33 Mach) Other speeds like bullet speed and canon speed can be simply googled. These, however, are the standards used in this wiki. Mathematical formulas of interest * Volume of a sphere = (4/3)*r^3*Pi * Chord method: R = (4*h^2+L^2)/8h (h is the height of the chord, L is the length and R is the radius of the circle) * Volume of a conical frustum = Pi*h*(R^2+Rr+r^2)/3 Useful calculators * Kinetic energy calculator * Projectile motion calculator * Free-fall calculator * Tsunami calculator * Category:Miscelaneous Category:Calc